# Add vector on vector's tip and rotation

Vector $v_1=[3,3,3],v_2=[1,0,0]$;

I mean adding vector upon vector with it's direction. Like $v1+v2$ wouldn't be $[4,3,3]$ but $[4,4,4]$.

Or another example $[1,2,0]+[0,3,0]$ will be around $[3,0,0]$. I don't know math very good but in my head I can explain it as "add vector upon vector on it's rotation/direction".

The question: How to add vector upon vector on it's direction?

Here is a picture for explain my question even better: http://i.stack.imgur.com/h0xsB.png

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What is your question? –  Joel Reyes Noche Nov 15 '12 at 12:58
@JoelReyesNoche How to add vector upon vector on it's direction. edited. –  FijiWiji Nov 15 '12 at 13:00
I don't see how your "addition" works. Can you give a picture or explanation of what exactly you want add? –  martini Nov 15 '12 at 13:08
It sounds like you're trying to describe complex multiplication in $3$ dimensions. There, if we multiply $z_1,z_2$, the magnitude is the product of the magnitudes, while the angle is the sum of the angles (so long as $z_1,z_2\neq0$). Am I correct? –  Cameron Buie Nov 15 '12 at 13:19
@CameronBuie Yeah, I think you're right. –  FijiWiji Nov 15 '12 at 13:21
$$u+|v|(u/|u|)$$
where $|\cdot|$ denotes the norm, i.e., $|u|=\sqrt{u_x^2+u_y^2+u_z^2}$.
Ok, then compute the length $a=|u+v|$; the vector you want is then $av/|v|$. –  PolyKnowMeAll Nov 15 '12 at 14:13